Question

The chord of contact of the tangents drawn from a point on the circle, $x^2+y^2=a^2$ to the circle $x^2+y^2=B^2$ touch the circle $x^2+y^2=c^2$ then a,b,c are in :

• A. A.P.
• B. G.P.
• C. H.P.
• D. $Noneofthese$

Answer 1

The correct option is B G.P.

Let $\left(x_1{y}_1\right)$ be any point on the circle $x^2+y^2=a^2$

$a_1^2+y_1^2=a^2$

$(x_1,y_1)$ to the circle $x^2+y^2=b^2$

tangent $x{x}_1+y{y}_1=b^2$

touches to the circle $x^2+y^2=a^2$

Length of $\perp$ from centre $(0,0)$ on $\left(2\right)$=radius

$\frac{b}{\sqrt{x_1^2+y_1^2}}=c$ or $\frac{b^2}{\sqrt{a^2}}=c$

$b^2=ac$

$abc$ are in $GP$